{
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4-final"
  },
  "orig_nbformat": 2,
  "kernelspec": {
   "name": "python_defaultSpec_1600520178904",
   "display_name": "Python 3.7.4 64-bit ('base': conda)"
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 },
 "nbformat": 4,
 "nbformat_minor": 2,
 "cells": [
  {
   "source": [
    "# scikit-learn中的多项式回归和Pipeline"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.uniform(-3, 3, size=100)\n",
    "X = x.reshape(-1,1)\n",
    "y = 0.5 * x**2 + x + 2 + np.random.normal(0 ,1, size =100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly = PolynomialFeatures(degree=2)\n",
    "poly.fit(X)\n",
    "X2 = poly.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(100, 3)"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "X2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 1.        , -0.27249181,  0.07425179],\n       [ 1.        , -0.82880496,  0.68691766],\n       [ 1.        , -1.64294546,  2.69926977],\n       [ 1.        , -0.39657179,  0.15726918],\n       [ 1.        ,  2.36944098,  5.61425054]])"
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "X2[:5,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[-0.27249181],\n       [-0.82880496],\n       [-1.64294546],\n       [-0.39657179],\n       [ 2.36944098],\n       [ 1.60272776]])"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "X[:6,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "lin_reg2 = LinearRegression()\n",
    "lin_reg2.fit(X2, y)\n",
    "y_predict2 = lin_reg2.predict(X2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(np.sort(x), y_predict2[np.argsort(x)], color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([0.        , 0.9487094 , 0.51899584])"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "lin_reg2.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1.88718438030803"
     },
     "metadata": {},
     "execution_count": 11
    }
   ],
   "source": [
    "lin_reg2.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "## PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.arange(1, 11).reshape(-1, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(5, 2)"
     },
     "metadata": {},
     "execution_count": 15
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[ 1,  2],\n       [ 3,  4],\n       [ 5,  6],\n       [ 7,  8],\n       [ 9, 10]])"
     },
     "metadata": {},
     "execution_count": 16
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly = PolynomialFeatures(degree=2)\n",
    "poly.fit(X)\n",
    "X2 = poly.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(5, 6)"
     },
     "metadata": {},
     "execution_count": 18
    }
   ],
   "source": [
    "X2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[  1.,   1.,   2.,   1.,   2.,   4.],\n       [  1.,   3.,   4.,   9.,  12.,  16.],\n       [  1.,   5.,   6.,  25.,  30.,  36.],\n       [  1.,   7.,   8.,  49.,  56.,  64.],\n       [  1.,   9.,  10.,  81.,  90., 100.]])"
     },
     "metadata": {},
     "execution_count": 19
    }
   ],
   "source": [
    "X2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly = PolynomialFeatures(degree=3)\n",
    "poly.fit(X)\n",
    "X3 = poly.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(5, 10)"
     },
     "metadata": {},
     "execution_count": 21
    }
   ],
   "source": [
    "X3.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[   1.,    1.,    2.,    1.,    2.,    4.,    1.,    2.,    4.,\n           8.],\n       [   1.,    3.,    4.,    9.,   12.,   16.,   27.,   36.,   48.,\n          64.],\n       [   1.,    5.,    6.,   25.,   30.,   36.,  125.,  150.,  180.,\n         216.],\n       [   1.,    7.,    8.,   49.,   56.,   64.,  343.,  392.,  448.,\n         512.],\n       [   1.,    9.,   10.,   81.,   90.,  100.,  729.,  810.,  900.,\n        1000.]])"
     },
     "metadata": {},
     "execution_count": 22
    }
   ],
   "source": [
    "X3"
   ]
  },
  {
   "source": [
    "## pipeline"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.uniform(-3, 3, size=100)\n",
    "X = x.reshape(-1,1)\n",
    "y = 0.5 * x**2 + x + 2 + np.random.normal(0 ,1, size =100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "poly_reg = Pipeline([(\"poly\", PolynomialFeatures(degree=2)),(\"std_scaler\", StandardScaler()),(\"lin_reg\", LinearRegression())])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly_reg.fit(X, y)\n",
    "y_predict = poly_reg.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(np.sort(x), y_predict[np.argsort(x)], color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}